Any headphone/earphone can be EQed to "precise and neutral" if the distortion is low enough. IEMs like the Etymotic IEMs often do well here, but if you dislike things inserted in your ear canal you might prefer planar magnetic headphones. These typically have lower distortion than dynamic drivers, especially in the bass. I have a set of HifiMan HE400se headphones, which used to be exceptionally good value before the price went up a lot recently.

To get the best possible results from equalization you need to do it by ear by comparison to a calibrated reference loudspeaker, but you can still get good results using other people's measurements. And there's no consensus what the best target curve is. Studio control rooms aren't anechoic chambers so "flat" won't necessarily give you the intended sound. You might find AutoEq useful:

https://autoeq.app/

I generally prefer no spatial processing, except in the case of 60s-style hard-panned stereo, which is intended for loudspeakers and does sound a lot better with the "earwax" filter or similar. "Precise and neutral" is a lot more difficult with loudspeakers, both because it's hard to keep distortion low when you're moving a lot of air, and because you have the off-axis response and room acoustics complicating things.